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# Re: [Phys-l] T dS versus dQ

• From: John Denker <jsd@av8n.com>
• Date: Wed, 13 Jan 2010 09:36:50 -0700

On 01/13/2010 08:19 AM, Carl Mungan wrote:

On the one hand, John M is correct that I was sloppy in stating that
-P dV is the work.

Well, if we can't be sure what "work" means in this
context, that's consistent with my longstanding contention
that "work" and "heat" are not trustworthy concepts. We
should concentrate on using terms and concepts we understand,
such as energy and entropy.
(I don't consider this the optimal example for illustrating
the point, but it is consistent with all the other examples.)

The work is positive but since I'm moving the
piston rapidly it cannot be easily calculated as an integral over the
actual process

Maybe not super-easy, but not really hard, either.
Strain gauges with sub-microsecond response times are
easy to come by.

but instead should be calculated from W = E_final -
E_initial which we can do because we have well-defined equilibrium
initial and final states.

That works, too. The astute experimenter would
measure both things:
-- energy input across the boundary of the region
-- delta energy content within the region
and verify that they agreed with each other.

... I think we *can* have irreversible infinitesimal
processes. It's just that dQ doesn't equal T dS *and* dW doesn't
equal -P dV for them.

I still don't think dQ exists. There is no Q function
with the required properties. d(anything) is an exact
one-form. dQ, if it existed, would be inexact (except
asking for the height of the water in Escher's Waterfall.
It cannot exist.
http://www.av8n.com/physics/thermo-forms.htm#fig-escher-waterfall

In far-from-equilibrium situations, T might be undefinable
and therefore we would be unable to calculate T dS. Still,
even then, S and dS would still exist. Energy and entropy
exist and are well behaved even in situations where the
temperature is irrelevant, unknown, and/or undefinable.

On 01/13/2010 09:11 AM, LaMontagne, Bob wrote:
... My claim was that
the final temperatures would be the same if the process proposed
would be done quickly or slowly.

The claim is still not true. Sudden movements of the piston
stir the gas. Stirring raises the temperature above what it
would have been without stirring.

Quickly is different from slowly. Stirred is different from
unstirred.